I think everyone has their ways of learning how to sing, but one thing is for sure: humans learn by mimicking what other humans do. This has been a very important part of my voice education after my teacher (a very good one) had taught me the basics.
She often uses a technique where she sings a straight, long note and asks me to sing the same long note with her and try to modify my voice so that it blends with her voice. In that way I have managed to increase the air flow in my voice, and get my voice to sound and ring more resonantly.
One thing that singing teachers constantly do wrong in their teaching is that they don't sit very close to the student if they sing and then ask the students to repeat the passage after their singing. In those situations, it is very helpful to sing for your student so that you are singing at most 20 centimeters from their ear. A good way is to go as close as possible to them and sing "past their ear".
You may ask why this is important: because this is the only way for your student to hear how much air you need to produce out when you are singing (especially classical singing). If you are singing to your student with the normal 2-3 meters between you and the student, they are not going to hear and learn the BIG amount of air flow that is needed for healthy singing. They will only hear the (usually) healthy and resonating voice and not distinguish the singing melody and the air flow that carries it. (You can clearly try and hear this yourself when you are yawning widely, a false yawn will probably suffice too - there is A LOT OF AIR coming out during the yawn - the same principle should be used in singing too.)